Triangle Calculator

How to use the triangle calculator

1. Enter the three side lengths.
2. Read the area and the three angles.
3. See the perimeter and the triangle type.
4. Copy the link to save or share it.

Solving a triangle from three sides

Three side lengths fix a triangle completely, so from them you can solve a triangle and find everything else. This triangle calculator works from the three sides and returns the triangle area, all three angles, the perimeter, and the type, giving the triangle sides and angles together, each triangle angle included. First it checks the sides can actually form a triangle, then applies two classic results to fill in the rest.

Heron's formula and the law of cosines

The area comes from Heron's formula: take the semi-perimeter s, which is half the sum of the sides, then the area is the square root of s times (s minus a) times (s minus b) times (s minus c). The angles come from the law of cosines, which relates each angle to the three sides, for example the cosine of angle A equals (b squared plus c squared minus a squared) divided by 2bc. Together they solve the triangle without needing a height.

The triangle inequality

Not every set of three lengths makes a triangle. Each side must be shorter than the other two added together, a rule called the triangle inequality. If it fails, for example sides of 1, 2, and 5, the pieces cannot meet to close the shape, and the tool tells you so instead of returning a meaningless answer.

A worked example

Take sides 3, 4, and 5. The semi-perimeter is 6. The area is the square root of 6 times 3 times 2 times 1, which is the square root of 36, so 6. The largest angle, opposite the side of 5, works out to exactly 90 degrees, so this is a right triangle.

FAQ

How do I find the area of a triangle from three sides?

Use Heron's formula: find the semi-perimeter, then take the square root of s times (s minus a) times (s minus b) times (s minus c). The tool does this for you.

How do I find the angles of a triangle?

Use the law of cosines, which gives each angle from the three side lengths. The tool reports all three angles in degrees.

What if the sides cannot form a triangle?

If any side is as long as or longer than the other two combined, no triangle exists. The tool checks this triangle inequality and flags it.

What makes a triangle right, acute, or obtuse?

Its largest angle: exactly 90 degrees is right, less than 90 is acute, and more than 90 is obtuse. The tool classifies the triangle by both its angles and its sides.

Is my information private?

Yes. Everything is calculated in your browser and nothing you enter is uploaded or saved.